Each dance has a unique character. The movements of each dance are intended to convey this character to onlookers. Rather than repeat all that has been said by others let me refer you to some other sources and I will add my own thoughts to help you understand. The character of certain dances may appeal to you more than some others.
This page at About.com offers thumbnail descriptions of 12 ballroom dances that may get you thinking about dance in new ways. This History of Ballroom Dance page describes number of dances with some historical notes. This page suggests that technique for International and North American styles is identical that is not strictly true. Furthermore, in the competitive forum, International Dance technique is much more strictly adjudicated than is North American.
My Commentary
It seems very likely that the first dance you will choose to learn is the one that appeals to the most. Visual appeal is always a strong force and the character of each dance is what creates its appearance. To look like the really good professional or top amateur dancers is a wonderful goal but social dancers rarely achieve such a goal. Never-the-less, well schooled social dancers can achieve enough of a dances character so as to look “really good” to almost everyone else.
If it is a smooth, sophisticated, elegance that appeals to you then waltz, viennese waltz, foxtrot and, perhaps, quickstep will likely attract your attention. Of these four you will find North American style foxtrot and either International or American style waltz most useful at public social dances. International style foxtrot could certainly be used in place of American style but the initial steps of the American style seem to be learned more easily.
The quickstep is simply spectacular. No other dance covers more dance floor more quickly and this quickness is an element that makes it difficult to learn and execute well. Since its steps are based upon the foxtrot, at least initially, knowing the foxtrot is of considerable value. The viennese waltz has a similar relationship to the waltz. It covers the dance floor almost as quickly as the quickstep and benefits from previous knowledge of the waltz. Viennese waltz exists in both American and International styles. The International style has about a dozen steps in the complete syllabus while the American style has many more and is very florid. The quickstep is danced only in the International style and the more advanced footwork is drawn more from the Lindy than from the foxtrot.
Tango is danced in many different styles. North American, International and Argentine styles are the most common and you can usually find good opportunities to dance in social settings. Tango is often described as a dance of fire, and passion. It is danced with stalking, catlike movements which include abrupt direction changes, rocking motions, sharp head movements and leg flicks. As you learn to dance the tango you discover the apparent sharpness of the dance is an illusion created more by the timing and synchronization of the partnership than by aggressive movements.
Compared to other ballroom dances, Latin dances are generally faster-paced, more sensual, and have more rhythmic expression. The latin dances are for couples, typically a man and a woman. Partners sometimes dance in a closed, tight position, and sometimes hold only one hand. Dramatic arm movements are common in most latin dances and create an additional complication as technique develops. Latin dancing, as Latin music, is sultry and physical. Quick paced rhythms and playful movements make the various Latin dances endlessly entertaining, sometimes even breathtaking.
Cha-Cha (sometimes referred to as cha cha cha) is a quick, energetic, fun dance. It is really hard to dance a cha cha without smiling. The latin motion is not the easiest technique to develop, particularly for men who may feel uncomfortable swinging their hips but it is great fun when you can begin to match your lady’s movements. This is a playful dance that can be danced to latin music and many popular tunes from several eras.
Rumba can be described by a whole collection of romantic adjectives. It is a slow, fun dance. The basics are easy to learn, however, more advanced technique is extremely challenging. Many rumba figures are flirtatious and teasing with the lady first approaching her partner then rejecting him and gliding away. The latin or Cuban hip motion is even more dramatic, although slower, in the rumba than the cha cha. Partners can make eye contact then turn away to emphasize the teasing aspect as the swaying hips and bodies intensify the sensuality.
Mambo and salsa are remarkably similar to each other and, indeed, the cha cha was derived from mambo. If, as a lady, you love to twirl and spin then these are the dances for you. Mambo is somewhat more structured than salsa but like the rumba and cha cha do not travel around the room but are danced in a relatively contained space. There are clubs virtually dedicated to salsa but mambo is not out of place. These dances can be learned quite quickly an even the elementary figures are quite showy.
There are several dances that are loosely grouped together as swing dances. The variations go under names such as Swing, East Coast Swing, West Coast Swing, Jive, Lindy Hop, and several others. Technically, Jive is a very fast, very high energy version most similar to East Coast Swing that is most often seen in competition rather than the social dance floor. Lindy is also quite high energy but it is common to find clubs that specialize in Lindy and other forms of swing. East and West Coast versions are the most common in social settings. East Coast Swing is danced more-or-less on-the-spot while West Coast Swing is danced on a straight line with partners exchanging positions and this is the most distinctive difference. The music is slightly slower for the West Coast Swing. Both of these forms are relatively easily learned.
Samba is a Brazilian party dance, very quick, very athletic, and very difficult to master. Fortunately, it can be great fun to dance even with less than a mastery. Perhaps the most difficult element to master is the “samba Bounce.” To be danced correctly, samba should appear to be effortless and the bounce must never be exaggerated. There will be some opportunity to practice at social dances and in some areas you may find clubs specializing in samba.
Paso Doble, although a Spanish name, actually had its origin in France It reflects a lively, march-like character where partners play different roles such as matador, matador’s cape or even the bull. It is most often choreographed for competition and very infrequently danced socially.